Aims

The project aims to give you some practice in crystal structure refinement from powder data by the Rietveld method. The data set has been chosen to illustrate certain points concerning use of the method, which should become apparent as you proceed with the project work. Angle-dispersive powder neutron diffraction data has been chosen since there are fewer problems due to texture or preferred orientation than would probably be encountered with x-ray data.

Background Information

The data was collected on the same sample of lead sulphate used in the case study for the Rietveld method section, but on this occasion collected at 5 K on the high-resolution powder diffractometer, D2B, at the ILL, Grenoble, with a nominal wavelength,

Instructions

1. If you do not have a Rietveld program on your PC, you will need to download one from the Internet.
2. Download the PbSO₄ at 5 K data.

   Column format based on 2q, intensity, and s

   Data file A (2q range is 8° to 62.475° with step 0.025°)
   Data file B (2q range 8° to 142.975° with step 0.025°)

3. Using the orthorhombic room-temperature structure of lead sulphate, refine the structure at 5 K with this model using the limited range of data provided by data set A. Write up the results including a plot of the best fit you can obtain. Since you may not be familiar with data from this diffractometer, approximate values for the resolution function parameters, UVW, are 0.05, -0.15, 0.20 (°²), respectively. The peak shape is nearly Gaussian (though with some imperfections due to defects in the original monochromator).
4. Using the refined model obtained above, calculate the diffraction pattern for the whole range of the data set B. Do not vary any of the parameters. Comment on the result and include a figure of the fit that you obtain.
5. For the remaining steps you should use the full data set B in your Rietveld refinements. The room-temperature structure of lead sulphate has the space-group symmetry Pbnm in which the sulphate anion has mirror-plane symmetry. One possible reason for the result observed in the preceding refinement is that a slight distortion of the unit cell occurs with consequent loss of the mirror-plane symmetry on cooling the sample to 5 K. The two lower-symmetry space groups of Pbnm that you will need to consider are therefore (i) P2₁/n and (ii) P2₁/b (with the symmetry elements relating to the x-axis). These are actually the same space group, but with different arrangements of the symmetry elements with respect to the unit-cell axes.
6. You should write up the results of the above refinements (in HTML) including appropriate tables of parameters and figures. You should discuss the differences in the structure of lead sulphate at 5 K and at 300 K.
7. In addition, at the end of your project report, you should also include a section containing refined parameters in the powder CIF format.